Problem $5.$ A database contains $100$ documents out of which only $10$ documents are relevant for a given

query. Two search engines, A and $B,$ report the following documents.

System A: RRNNNRNNNR RNNRNNNNRN NNRNNNNNRN and so on

System B: RRRNNNNNNN NRRNNNNNNR NNNNNRNNNN and so on

where $R$ represents relevant document and $N$ represents Non$-$relevant document. A search engine expert

wants to estimate the accuracy of both these systems by computing the following information, so that,

he can know how many documents to display.

$($a$)$ Using the PR$-$Curve info, compute the Precision at $40\%$ Recall.

$($b$)$ If the expert decides to display only the first $15$ documents for both of these search engines,

calculate Precision, Recall and F$-$measure.

$(20$ Points; $10$ pts each$)$